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11 Sep 2016, 16:09

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67%(01:33) correct 33%(01:26) wrong based on 184 sessions

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The figure shown is a regular hexagon with center h. the shaded area is a parallelogram that shares three vertices with the hexagon and its fourth vertex is the center of the hexagon. If the length of one side of the hexagon is 8 centimeters, what is the area of the unshaded region?

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11 Sep 2016, 17:30

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azamaka wrote:

The figure shown is a regular hexagon with center h. the shaded area is a parallelogram that shares three vertices with the hexagon and its fourth vertex is the center of the hexagon. If the length of one side of the hexagon is 8 centimeters, what is the area of the unshaded region?

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11 Sep 2016, 18:47

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Hi azamaka,

For future reference, any time a GMAT question includes a 'weird' shape, chances are really good that you can 'break down' that shape into smaller shapes that you DO know (re: right triangles, rectangles, etc.). Here, we have a regular hexagon, which is certain weird. Regular hexagons can be broken down into 6 equilateral triangles and (if you find it necessary), each equilateral triangle can be broken down into two 30/60/90 right triangles. Thankfully, the GMAT won't make you deal with this type of weird Geometry very often. If you do face this type of situation on Test Day, and you decide to spend time on the prompt (as opposed to dumping it), you'll likely need to spend a bit more time (than average) answering the question and you should look for ways to break the shape(s) down into pieces.

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13 Nov 2017, 12:53

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azamaka wrote:

The figure shown is a regular hexagon with center h. the shaded area is a parallelogram that shares three vertices with the hexagon and its fourth vertex is the center of the hexagon. If the length of one side of the hexagon is 8 centimeters, what is the area of the unshaded region?

This prompt's wording and wordiness could confuse. The figure is better. Unshaded region area = (hexagon area) - (parallelogram area)

Dividing shapes into triangles is an easy way to find area, especially when the polygons are regular (equal angles, equal sides).

A regular polygon can be divided into congruent isosceles triangles.A regular hexagon is the only regular polygon that can be divided into congruent equilateral triangles.

Connect the vertices. There are 6 equilateral triangles.

An equilateral triangle has three 60° angles.Six sides of a hexagon divide 360° at center into six 60° angles at center The other two angles of each triangle also = 60°; both bisect a vertex of 120° = 60° each

Given: each side of hexagon = 8 cmFrom above: the six triangles are equilateral. Each side of each triangle = 8 cm

Find the area of one of these triangles. Multiply by 6 for the area of the hexagon. Multiply by 2 for the area of the parallelogram, which = two of those triangles